Section 7-3 Solve Systems by EliminationSPI 23D: select the system of equations that could be used to solve a given real-world

problem

Objective:• Solve systems of linear equations by elimination

Three Methods of solving Systems of Equations:

• Solve by Graphing• Solve by Substitution• Solve by Elimination

Solve a System of Linear Equations by Elimination

Elimination: Solve systems of equations by using the Properties of Equality (add or subtract equations)

Solve the system of linear equations using elimination 6x – 3y = 3-6x + 5y = 3

1. Add the two equations and eliminate x because the sum of the coefficients is 0.

6x – 3y = 3-6x + 5y = 3 0 + 2y = 6

2. Solve for the remaining variable by using either equation.y = 3

6x – 3y = 3 6x – 3(3) = 3 6x = 12 x = 2

Solve a System of Linear Equations by Elimination

Sometimes it is necessary to first, multiply one or both equations by a number to make the coefficients have a sum of zero.

Solve the system of linear equations using elimination-2x + 15y = -32 7x – 5y = 17

-2x + 15y = -327x – 5y = 17

1. Multiply bottom equation by 3, to make coefficients of y equal 0.

-2x + 15y = -323(7x – 5y = 17)

-2x + 15y = -3221x – 15y = 51)

2. Subtract to eliminate y. 19x = 19

3. Solve for x and substitute into either equation to find y.

-2x + 15y = -32 -2(1) + 15y = -32y = -2

x = 1

Real-world and Systems of Equations Two groups of students order burritos and tacos at a

restaurant. One order of 3 burritos and 4 tacos costs $11.33. The other order of 9 burritos and 5 tacos costs $23.56.

Write a system of equations to model the problem.

Solve by elimination to find the cost of a burrito and the cost of a taco.

3b + 4t = 11.339b + 5t = 23.56

3b + 4t = 11.339b + 5t = 23.56

-3(3b + 4t = 11.33) 9b + 5t = 23.56

-9b - 12t = -33.99 9b + 5t = 23.56

-7t = -10.43t = 1.49

3b + 4(1.49) = 11.33 3b + 5.96 = 11.33 3b = 5.37 b = 1.79 A taco costs $1.49 and a burrito cost $1.79